三组以上治疗方案时，自适应试验比完全随机试验更优。
Admissibility of Completely Randomized Trials: A Large-Deviation Approach
- 采用分批淘汰法逐步剔除效果差的治疗组
- 当治疗组≥3时，自适应设计效率显著高于随机试验
- 适用于需高效筛选最优治疗方案的研究场景
当实验者可选择自适应试验时，忽略该选项而采用非自适应试验是否合理？在最佳治疗臂识别问题中，我们给出否定回答：只要治疗臂不少于三个，就存在简单自适应设计能普遍且严格优于完全随机试验。这种优势由效率指数刻画，反映大样本下的统计效率。研究聚焦于分批淘汰设计，即在预设批次间隔中逐步淘汰表现较差的臂。我们给出了这些设计普遍严格优于完全随机试验的充分条件。该成果解决了Qin [2022]提出的第二个开放问题。
原文摘要 · Abstract (English)
When an experimenter has the option of running an adaptive trial, is it admissible to ignore this option and run a non-adaptive trial instead? We provide a negative answer to this question in the best-arm identification problem, where the experimenter aims to allocate measurement efforts judiciously to confidently deploy the most effective treatment arm. We find that, whenever there are at least three treatment arms, there exist simple adaptive designs that universally and strictly dominate non-adaptive completely randomized trials. This dominance is characterized by a notion called efficiency exponent, which quantifies a design's statistical efficiency when the experimental sample is large. Our analysis focuses on the class of batched arm elimination designs, which progressively eliminate underperforming arms at pre-specified batch intervals. We characterize simple sufficient conditions under which these designs universally and strictly dominate completely randomized trials. These results resolve the second open problem posed in Qin [2022].
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